Laplacian Risk Management

Abstract

Risk management is developed by using implied volatilities associated with a Laplacian base density as opposed to the normal distribution. Expressions are derived for all the Laplacian greeks. The Laplacian implied volatilities and greeks are compared with their Gaussian counterparts. Differences in hedges are illustrated by hedging long dated straddles using short maturity options. The Laplacian hedge delivers cash flows with a lower final variability in the case presented. The computation speed of Laplacian entities is also observed to be substantially faster as there are no calls to the cumnorm function.

Keywords: Local Volatility, Compound Poisson, Theta, Gamma, Vega, Volga and Vanna

JEL Classification: G10, G13